Last year, Ken bought a mountain bike for $460. His bike has depreciated since he bought it. It is now worth $320. About what percent did the value of Ken’s bike depreciate over the past year?

Answer 1

To find the percent depreciation of Ken's bike, we first need to calculate the amount of depreciation and then determine what percent that is of the original value.

1. Calculate the amount of depreciation: $$\text{Depreciation}=\text{Original Value}-\text{Current Value}=460-320=140$$

2. Calculate the percent depreciation: $$\text{Percent Depreciation}=\left(\frac{\text{Depreciation}}{\text{Original Value}}\right)\times 100=\left(\frac{140}{460}\right)\times 100$$

3. Calculate the fraction and then the percentage: $$\frac{140}{460}=0.3043478261(\text{approximately})$$ Now, multiplying by 100 to get the percentage: $$0.3043478261\times 100\approx 30.43$$

Thus, the value of Ken's bike has depreciated by approximately 30.43% over the past year.

In summary, about 30.4%.